Question

A circle and a squre have the same perimeter. Then:

• A. there areas are equal
• B. the area of the circle is the greater
• C. the area of the square is the greater
• D. the area of the circle is x times the area of the square
• E. none of these

Answer 1

Answer: (B)

the area of the circle is the greater

Perimeter of the circle = Perimeter of the square

$2\pi r=4a\therefore r=\frac{2a}{\pi }$

Area of the circle = $\pi r^2=\frac{4a^2}{\pi }$

Area of the square= $a^2$

$\frac{4}{\pi }>1$

Therefore, area of the circle is greater than the area of the square.